Hemlock is one of the more refined barks for mulch in the northeastern part of the United States. It smells nice and has a rusty red color which takes a while to fade. There are some bark chips that are artificially colored a deep red, and these are more expensive. It is simply personal aesthetic preference.
Oak and birch are hardwoods that are sometimes used for bark mulch. According to Gordon Hayward, author of the book "Garden Paths," oak from the debarker is typically shot through with long, broad, unattractive strips. White birch is more attractive, though it too has many long strips of papery bark in the mix. Some people may like this look, while others may feel it requires extra time to remove those strips. Hardwood mulch, once the stray strips are removed, is highly attractive, lasts a long time, and makes an efficient weed barrier.
The least inexpensive type of mulch is made up of various pine bark peelings. A layer that is 2 to 3 inches of pine bark mulch can make a good weed barrier. It is darker in color than some bark mulches and can be bought in a finely shredded form up to a large chip-sized form. The finer the bark mulch, the more moisture it will hold, so if you are looking to use it for the base of plants and trees, finer mulch is what you want. If you are looking to fill an area such as garden edging, larger sized mulch will fill the area easier, though these are more easily displaced by heavy storms. Pine needles allow water to easily penetrate them and make good mulch as well, especially as a cover around acid loving trees.
Cedar is a much sought-after wood for outdoor purposes such as mulch because it has natural oils that help to repel insects like termites, but it is more costly for this reason. It is also highly weather resistant and has a beautiful, natural light-red color that many people prefer for their garden, and will change color with time to a paler brown color.